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I don't believe they would determine or even expect it is following an algorithm.

For example on HN my password could be 1YCju7i8!

It isn't, but let's pretend it is.

That is a counter at the front, YC is from the website address, j from my user name, and u7i8! It's the unique key. I use the same key everywhere so it's easy to remember.

I don't think a hacker would figure it out.

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Two websites breaches and they already have your 'unique key' (which is not unique if its the same for every website.

Yes it's just unique for the 'user' of the Algorithm.

I think you have a valid point in multi site leaks if the attacker was focused on my account. I will think about it

and to an extend how do you keep track of which unique part is active in which site if e.g a website gets hacked and resets your current password, because in case of a password manager i just create a new one and be done, on top of my mind i would have the question for you: would you recreate all websites with a new unique part or just create a system for outliers? not to offend, just had several of these incidents in my years and for me a password manager is much more piece of mind

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